Question: Simplify the following expression: $ t = \dfrac{x - 10}{x - 6} + \dfrac{9}{10} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{x - 10}{x - 6} \times \dfrac{10}{10} = \dfrac{10x - 100}{10x - 60} $ Multiply the second expression by $\dfrac{x - 6}{x - 6}$ $ \dfrac{9}{10} \times \dfrac{x - 6}{x - 6} = \dfrac{9x - 54}{10x - 60} $ Therefore $ t = \dfrac{10x - 100}{10x - 60} + \dfrac{9x - 54}{10x - 60} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{10x - 100 + 9x - 54}{10x - 60} $ $t = \dfrac{19x - 154}{10x - 60}$